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(2) 1-2 st 32 sec Given: xi(t) = {0 elsewhere and xz(t) = {o -2 st...
(b) Consider continuous-time signals xi(t) and x2(t) respectively given as (t +1 -1 <t<o x1(t) =...
(b) Consider continuous-time signals xi(t) and x2(t) respectively given as (t +1 -1 <t<o x1(t) = { 2 Ost<2 , I 0 otherwise x2(t) = u(t) – uſt – 2). Find the convolution xı(t) * x2(t). (15 marks)
Consider the following. Xi' = 3x1 - 2x2 x1(0) = 3 xz' = 2x1 – 2x2,...
Consider the following. Xi' = 3x1 - 2x2 x1(0) = 3 xz' = 2x1 – 2x2, *2(0) = (a) Transform the given system into a single equation of second order by solving the first equation for x2 and substitute into the second equation, thereby obtaining a second order equation for X1. (Use xp1 for xı' and xpP1 for x1".) xpP1 – xP1 – 2x1 = 0 (b) Find X1 and x2 that also satisfy the initial conditions. *2(t) =
1) Given the functions xi()-tu()-tu(t-I) and xz()-10e "u(), do the following: Find x()-x(0)*xz() by hand using Laplace transforms. 1) Given the functions xi()-tu()-tu(t-I) and xz()-10e &...
1) Given the functions xi()-tu()-tu(t-I) and xz()-10e "u(), do the following: Find x()-x(0)*xz() by hand using Laplace transforms.
1) Given the functions xi()-tu()-tu(t-I) and xz()-10e "u(), do the following: Find x()-x(0)*xz() by hand using Laplace transforms.
anwer this ..The answer must be?? 2.3.3 Let f(2), 0 of Xi and X2. 1, zero...
anwer this ..The answer must be??
2.3.3 Let f(2), 0 of Xi and X2. 1, zero elsewhere, be the joint podf of X1 and X2 (a) Find the conditional mean and variance of X1, given X2 = 22, 0 < x2 < 1. (b) Find the distribution of Y E(X1|X2). (c) Determine E(Y) and Var(Y) and compare these to E(X1) and Var(X1), Te spectively
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using convolution integral method. b) Compute g*f () with Laplace transform. o) What are the differences between the results of questions (a)...
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using convolution integral method. b) Compute g*f () with Laplace transform. o) What are the differences between the results of questions (a) and (0) above? d) Find the Laplace transform of the following function: (t 0 to +oo) e dt e) Find the equivalent solution of (d) using MATLAB method) (find 2 methods)
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using...
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i + 2, for i = 0, . . . , 3. Given the divided difference...
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i
+ 2, for i = 0, . . . , 3. Given the divided differences f[x0] = 1,
f[x0, x1] = 2, f[x0, x1, x2] = −7, f[x0, x1, x2, x3] = 9, add the
data point (0, 3), find a Newton form for the Lagrange polynomial
interpolating all 5 data points.
3. (25 pts) Let (r,, f()), 0,3, be data...
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal x(t) is X(f) - rect(f/ 2), find the Fourier Transform of the following signals using properties of the Fourier...
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal x(t) is X(f) - rect(f/ 2), find the Fourier Transform of the following signals using properties of the Fourier Transform: (a) d(t) -x(t - 2) (d) h(t) = t x( t ) (e) p(t) = x( 2 t ) (f) g(t)-x( t ) cos(2π) (g) s(t) = x2(t ) (h)p()-x(1)* x(t) (convolution)
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal...
2. Calculate the inverse Fourier transform of X(cfw) = {2 2j 0 <W <T -2j -n<w...
2. Calculate the inverse Fourier transform of X(cfw) = {2 2j 0 <W <T -2j -n<w < 3. Given that x[n] has Fourier transform X(@j®), express the Fourier transforms of the following signals in terms of X(el“) using the discrete-time Fourier transform properties. (a) x1[n] = x[1 – n] + x[-1 - n] (b) x2 [n] = x*[-n] + x[n]
4. X(c)-1 for lol < 5 and is zero elsewhere. Use the theorems to find and...
4. X(c)-1 for lol < 5 and is zero elsewhere. Use the theorems to find and sketch the amplitude versus ω and the phase angle versus ω of the transforms of the following signals. (a) t0, (b, (e) x(2), and (e) x() expG10) dx(t) dt' TABLEme Selected Properties of the Fourier Transform X (o) 2. 3. x(-t) X (-o) 5. x(-o) x (at) la l 8. lx ()12 dr x(t)h(C) x (t) 9. 10. 2π X (ω-@g) d"X (0) 12....
3. Find it) vo 412 w X 2/4) t=0 sec LE 320 zov 2 4.- (25)...
3. Find it) vo 412 w X 2/4) t=0 sec LE 320 zov 2 4.- (25) Find itt) two ways: a) in the time domain 6) using the Laplace Transform t=0 sec et ilt) + 10 cost Volts 12 mm lovolts MI
(b) Consider continuous-time signals xi(t) and x2(t) respectively given as (t +1 -1 <t<o x1(t) = { 2 Ost<2 , I 0 otherwise x2(t) = u(t) – uſt – 2). Find the convolution xı(t) * x2(t). (15 marks)
Consider the following. Xi' = 3x1 - 2x2 x1(0) = 3 xz' = 2x1 – 2x2, *2(0) = (a) Transform the given system into a single equation of second order by solving the first equation for x2 and substitute into the second equation, thereby obtaining a second order equation for X1. (Use xp1 for xı' and xpP1 for x1".) xpP1 – xP1 – 2x1 = 0 (b) Find X1 and x2 that also satisfy the initial conditions. *2(t) =
1) Given the functions xi()-tu()-tu(t-I) and xz()-10e "u(), do the following: Find x()-x(0)*xz() by hand using Laplace transforms.
1) Given the functions xi()-tu()-tu(t-I) and xz()-10e "u(), do the following: Find x()-x(0)*xz() by hand using Laplace transforms.
anwer this ..The answer must be??
2.3.3 Let f(2), 0 of Xi and X2. 1, zero elsewhere, be the joint podf of X1 and X2 (a) Find the conditional mean and variance of X1, given X2 = 22, 0 < x2 < 1. (b) Find the distribution of Y E(X1|X2). (c) Determine E(Y) and Var(Y) and compare these to E(X1) and Var(X1), Te spectively
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using convolution integral method. b) Compute g*f () with Laplace transform. o) What are the differences between the results of questions (a) and (0) above? d) Find the Laplace transform of the following function: (t 0 to +oo) e dt e) Find the equivalent solution of (d) using MATLAB method) (find 2 methods)
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using...
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i
+ 2, for i = 0, . . . , 3. Given the divided differences f[x0] = 1,
f[x0, x1] = 2, f[x0, x1, x2] = −7, f[x0, x1, x2, x3] = 9, add the
data point (0, 3), find a Newton form for the Lagrange polynomial
interpolating all 5 data points.
3. (25 pts) Let (r,, f()), 0,3, be data...
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal x(t) is X(f) - rect(f/ 2), find the Fourier Transform of the following signals using properties of the Fourier Transform: (a) d(t) -x(t - 2) (d) h(t) = t x( t ) (e) p(t) = x( 2 t ) (f) g(t)-x( t ) cos(2π) (g) s(t) = x2(t ) (h)p()-x(1)* x(t) (convolution)
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal...
2. Calculate the inverse Fourier transform of X(cfw) = {2 2j 0 <W <T -2j -n<w < 3. Given that x[n] has Fourier transform X(@j®), express the Fourier transforms of the following signals in terms of X(el“) using the discrete-time Fourier transform properties. (a) x1[n] = x[1 – n] + x[-1 - n] (b) x2 [n] = x*[-n] + x[n]
4. X(c)-1 for lol < 5 and is zero elsewhere. Use the theorems to find and sketch the amplitude versus ω and the phase angle versus ω of the transforms of the following signals. (a) t0, (b, (e) x(2), and (e) x() expG10) dx(t) dt' TABLEme Selected Properties of the Fourier Transform X (o) 2. 3. x(-t) X (-o) 5. x(-o) x (at) la l 8. lx ()12 dr x(t)h(C) x (t) 9. 10. 2π X (ω-@g) d"X (0) 12....
3. Find it) vo 412 w X 2/4) t=0 sec LE 320 zov 2 4.- (25) Find itt) two ways: a) in the time domain 6) using the Laplace Transform t=0 sec et ilt) + 10 cost Volts 12 mm lovolts MI
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